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Multi-Objective Bayesian Optimization

Most optimization problems involve a single measurable objective (yield, selectivity, conversion). However, many real experimental systems require balancing multiple competing objectives simultaneously — for example, maximizing yield while minimizing cost, or maximizing selectivity while maintaining throughput.

ALchemist supports multi-objective Bayesian optimization (MOBO), providing Pareto frontier visualization and hypervolume-based convergence tracking.

Core Concepts

The Pareto Frontier

When optimizing multiple objectives, there is rarely a single "best" solution. Instead, there is a Pareto frontier — the set of solutions where improving one objective necessarily worsens another.

A solution is Pareto-optimal if no other feasible solution is better on at least one objective without being worse on any other.

Example: Maximizing both yield and selectivity simultaneously. Higher yield often comes at the cost of lower selectivity (e.g., broader operating conditions). The Pareto frontier maps the achievable trade-off curve.

Hypervolume

The hypervolume (or S-metric) measures the volume of the objective space dominated by the current Pareto frontier, relative to a reference point. It is a scalar convergence metric:

  • Increasing hypervolume → the Pareto frontier is expanding (more experiments finding better trade-offs)
  • Plateauing hypervolume → the frontier is well-characterized; further experiments offer diminishing returns

Setting Up Multi-Objective Optimization

Step 1: Define Your Variables

Set up your variable space as usual. Multi-objective workflows use the same Real, Integer, Categorical, and Discrete variable types.

Step 2: Load Data with Multiple Target Columns

Your CSV file should have one column per objective, each containing numeric measurements.

Example CSV: 

Temperature,Pressure,Catalyst,Yield,Selectivity
250,10,Ni,0.72,0.91
300,15,Pt,0.85,0.78
...

When uploading data in the web UI:

  1. Click Load Experiments.
  2. After selecting your CSV, a Target Column Selection panel appears showing all available columns.
  3. Select the columns that represent your optimization objectives (e.g., Yield and Selectivity).
  4. Columns not selected and not matching variable names are treated as dropped columns (ignored).
  5. Click Load.

Step 3: Configure Target Column Roles

Each column in your dataset can be assigned one of three roles:

Role Description
Variable Controllable input (matches your variable space definition)
Target Measured output to optimize — one per objective
Drop Metadata column to ignore (e.g., experiment date, run ID)

In the web UI, column roles are assigned automatically where names match your variable space, and you select targets from the remaining columns.

Python API

from alchemist_core import OptimizationSession

session = OptimizationSession()
session.add_variable("Temperature", "real", min=200, max=400)
session.add_variable("Pressure", "real", min=5, max=30)
session.add_variable("Catalyst", "categorical", categories=["Ni", "Pt", "Pd"])

# Load data with multiple target columns
session.load_data(
    "my_experiments.csv",
    target_columns=["Yield", "Selectivity"]
)

REST API

POST /api/v1/sessions/{session_id}/experiments/upload?target_columns=Yield,Selectivity
Content-Type: multipart/form-data

The target_columns parameter accepts a single column name or comma-separated names for multi-objective.

Visualizations

Pareto Plot

The Pareto plot shows the experimental data projected onto two objective dimensions, highlighting which experiments lie on the Pareto frontier.

  • Pareto-optimal points are marked distinctly from dominated solutions
  • Helps visualize the current trade-off curve and identify gaps to explore

Access in the web UI from the Visualizations panel → Pareto Plot.

Hypervolume Convergence Plot

Tracks the hypervolume of the Pareto frontier across iterations. A rising curve indicates the active learning loop is making progress; a plateau suggests convergence.

Access from Visualizations → Hypervolume Convergence.

Desktop GUI

The desktop application includes a dedicated Multi-Objective panel that becomes active when multiple target columns are loaded. From this panel you can:

  • View the current Pareto frontier
  • See which experiments are Pareto-optimal
  • Inspect trade-off relationships between objectives

Current Scope

MOBO in ALchemist is currently Phase 1 (visualization and data infrastructure):

  • ✅ Multi-target column loading
  • ✅ Pareto frontier computation and visualization
  • ✅ Hypervolume convergence tracking
  • ✅ Desktop and web UI panels for MOBO data

Multi-objective acquisition functions (e.g., qEHVI, qNEHVI) for active Pareto improvement are planned for a future release.

Tips

  • Choose objectives carefully: Conflicting objectives (negatively correlated) produce meaningful Pareto frontiers. Aligned objectives (positively correlated) do not require MOBO — optimize one as a proxy.
  • Normalize objectives: If objectives have very different scales, consider normalizing before interpretation, though ALchemist handles this internally for hypervolume computation.
  • Reference point: The hypervolume is computed relative to an anti-ideal reference point derived from the worst observed values. Results are comparable within a session but not across sessions with different data scales.